In materials science, fatigue is the progressive, localised, and permanent structural damage that occurs when a material is subjected to cyclic or fluctuating strains at nominal stresses that have maximum values less than (often much less than) the static yield strength of the material. The resulting stress may be below the ultimate tensile stress, or even the yield stress of the material, yet still cause catastrophic failure. In engineering, buckling is a failure mode characterised by a sudden failure of a structural member that is subjected to high compressive stresses where the actual compressive stresses at failure are smaller than the ultimate compressive stresses that the material is capable of withstanding. ... Corrosion is deterioration of essential properties in a material due to reactions with its surroundings. ... In materials science, creep is the term used to describe the tendency of a material to move or to deform permanently to relieve stresses. ... For fractures in geologic formations, see Rock fracture. ... In physics, melting is the process of heating a solid substance to a point (called the melting point) where it turns into a liquid. ... Thermal shock is the name given to cracking as a result of rapid temperature change. ... In materials science, wear is the erosion of material from a solid surface by the action of another solid. ... The Materials Science Tetrahedron, which often also includes Characterization at the center Materials science is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. ... Stress is the internal distribution of force per unit area that balances and reacts to external loads applied to a body. ... Tensile strength measures the force required to pull something such as rope, wire, or a structural beam to the point where it breaks. ... Tensile strength measures the force required to pull something such as rope, wire, or a structural beam to the point where it breaks. ...

A practical example of low-cycle fatigue would be the bending of a paperclip. A metal paperclip can be bent past its yield point (i.e., bent so it will stay bent) without breaking, but repeated bending in the same section of wire will cause the material to fail.

Characteristics of fatigue failures

The following characteristics are common to fatigue in all materials:

• The process starts with a microscopic crack, called the initiation site, which then widens with each subsequent movement, a phenomenon analysed in the topic of fracture mechanics.
• Failure is essentially probabilistic. The number of cycles required for failure varies between homogeneous material samples. Analysis demands the techniques of survival analysis.
• The greater the applied stress, the shorter the life.
• Damage is cumulative. Materials do not recover when rested.
• Fatigue life is influenced by a variety of factors, such as temperature and surface finish, in complicated ways.
• Some materials (e.g., some steel and titanium alloys) exhibit an endurance limit or fatigue limit, a limit below which repeated stress does not induce failure, theoretically, for an infinite number of cycles of load. Most other non-ferrous metals (e.g., aluminium and copper alloys) exhibit no such limit and even small stresses will eventually cause failure.
• As a means to gauge fatigue characteristics of non-ferrous and other alloys that do not exhibit an endurance limit, a fatigue strength is frequently determined, and this is typically the stress level at which a component will survive 10⁷ loading cycles.

This does not cite its references or sources. ... Probability is the extent to which something is likely to happen or be the case[1]. Probability theory is used extensively in areas such as statistics, mathematics, science, philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems. ... Survival analysis is a branch of statistics which deals with death in biological organisms and failure in mechanical systems. ... Fig. ... Roughness or rugosity is a measurement (see surface metrology) of the small-scale variations in the height of a physical surface. ... The old steel cable of a colliery winding tower Steel is an alloy whose major component is iron, with carbon content between 0. ... General Name, Symbol, Number titanium, Ti, 22 Chemical series transition metals Group, Period, Block 4, 4, d Appearance silvery metallic Atomic mass 47. ... General Name, Symbol, Number aluminium, Al, 13 Chemical series poor metals Group, Period, Block 13, 3, p Appearance silvery Atomic mass 26. ... General Name, Symbol, Number copper, Cu, 29 Chemical series transition metals Group, Period, Block 11, 4, d Appearance metallic pinkish red Atomic mass 63. ...

Timeline of early fatigue history

• 1837: Wilhelm Albert publishes the first article on fatigue. He devised a test machine for conveyor chains used in the Clausthal mines.^[1]

• 1839: Jean-Victor Poncelet describes metals as being tired in his lectures at the military school at Metz.

Typical example of fatigue failure in an axle

• 1842: William John Macquorn Rankine^[2] recognises the importance of stress concentration in his investigation of railroad axle failures following the Versailles accident.

• 1849: Eaton Hodgkinson is granted a small sum of money to report to the UK Parliament on his work in ascertaining by direct experiment, the effects of continued changes of load upon iron structures and to what extent they could be loaded without danger to their ultimate security.

• 1854: Braithwaite^[3] reports on common service fatigue failures and coins the term fatigue.
• 1860: Systematic fatigue testing undertaken by Sir William Fairbairn and August Wöhler.

• 1870: Wöhler summarises his work on railroad axles. He concludes that cyclic stress range is more important than peak stress and introduces the concept of endurance limit.^[1]

Fatigue cracks from Ewing & Humfrey (1903)

• 1903: Sir James Alfred Ewing demonstrates the origin of fatigue failure in microscopic cracks.
• 1910: O. H. Basquin proposes a log-log relationship for SN curves, using Wöhler's test data.
• 1945: A. M. Miner popularises A. Palmgren's (1924) linear damage hypothesis as a practical design tool.
• 1954: L. F. Coffin and S. S. Manson explain fatigue crack-growth in terms of plastic strain in the tip of cracks.
• 1961: P. C. Paris proposes methods for predicting the rate of growth of individual fatigue cracks in the face of initial scepticism and popular defence of Miner's phenomenological approach.
• 1968: Tatsuo Endo and M. Matsuiski devise the rainflow-counting algorithm and enable the reliable application of Miner's rule to random loadings.
• 1970: W. Elber elucidates the mechanisms and importance of crack closure.

Wilhelm August Julius Albert (January 24, 1787 - July 4, 1846) was a German mining adminstrator, best remembered as the first person to record observations of metal fatigue. ... Point of contact between a power transmission belt and its pulley A conveyor belt or belt conveyor consists of two end pulleys, with a continuous loop of material that rotates about them. ... Clausthal-Zellerfeld is a town in Lower Saxony, Germany. ... This article is about mineral extraction. ... Jean-Victor Poncelet (July 1, 1788 РDecember 22, 1867) was a mathematician and engineer who did much to revive projective geometry. ... For other uses of Metz, see Metz (disambiguation) City motto: Si paix dedans, paix dehors (French: If peace inside, peace outside) City proper (commune) R̩gion Lorraine D̩partement Moselle (57) Mayor Jean-Marie Rausch Area 41. ... Historic line drawing of railway axle fatigue. ... Historic line drawing of railway axle fatigue. ... William John Macquorn Rankine (July 2, 1820 - December 24, 1872) was a Scottish engineer and physicist. ... A stress concentration is a phenomenon encounterered in mechanical engineering where an object under load has higher than average local stresses due to its shape. ... This is the top-level page of WikiProject trains Rail tracks Rail transport refers to the land transport of passengers and goods along railways or railroads. ... An axle is a central shaft for a rotating wheel or gear. ... In materials science, fatigue is the progressive, localized, and permanent structural damage that occurs when a material is subjected to cyclic or fluctuating strains at nominal stresses that have maximum values less than (often much less than) the static yield strength of the material. ... Eaton A. Hodgkinson (February 26, 1789 - June 18, 1861) was an English engineer, a pioneer of the application of mathematics to problems of structural design. ... The Parliament of the United Kingdom of Great Britain and Northern Ireland is the supreme legislative institution in the United Kingdom and British overseas territories (it alone has parliamentary sovereignty). ... Sir William Fairbairn Sir William Fairbairn (February 19, 1789 - August 18, 1874) was a Scottish engineer. ... August W̦hler (June 22, 1819 - March 21, 1914) was a German engineer, best remembered for his systematic investigations of metal fatigue. ... Classis historic discovery of role of microscopic cracks in fatigue of metals, Philosophical Transactions of the Royal Society, 1903 This work is copyrighted. ... Classis historic discovery of role of microscopic cracks in fatigue of metals, Philosophical Transactions of the Royal Society, 1903 This work is copyrighted. ... Sir James Alfred Ewing (March 27, 1855 - January 7, 1935) was a British physicist and engineer, best known for his work on the magnetic properties of metals and, in particular, for his discovery of, and coinage of the word, hysteresis. ... Year 1924 (MCMXXIV) was a leap year starting on Tuesday (link will display the full calendar). ... For other uses, see Plasticity. ... Look up strain in Wiktionary, the free dictionary. ... Tatsuo Endo (1925 - 1989) was a Japanese engineer who, in 1968 along with M. Matsuiski, developed the rainflow-counting algorithm for fatigue analysis of structures while a visiting professor at the University of Illinois. ... Figure 1: Uniform alternating loading The rainflow-counting algorithm (also known as the rain-flow counting method) is used in the analysis of fatigue data in order to reduce a spectrum of varying stress into a set of simple stress reversals. ... Random redirects here. ...

High-cycle fatigue

Historically, most attention has focused on situations that require more than 10⁴ cycles to failure where stress is low and deformation primarily elastic. Elasticity has meanings in two different fields: In physics and mechanical engineering, the theory of elasticity describes how a solid object moves and deforms in response to external stress. ...

The S-N curve

In high-cycle fatigue situations, materials performance is commonly characterised by an S-N curve, also known as a Wöhler curve. This is a graph of the magnitude of a cyclical stress (S) against the cycles to failure (N).

Image File history File links BrittleAluminium320MPA_S-N_Curve. ...

S-N curves are derived from tests on samples of the material to be characterised (often called coupons) where a regular sinusoidal stress is applied by a testing machine which also counts the number of cycles to failure. This process is sometimes known as coupon testing. Each coupon test generates a point on the plot though in some cases there is a runout where the time to failure exceeds that available for the test (see censoring). Analysis of fatigue data requires techniques from statistics, especially survival analysis and linear regression. A sine wave or sinusoid is a waveform whose graph is identical to the generalized sine function y = Asin[ω(x − α)] + C where A is the amplitude, ω is the angular frequency (2π/P where P is the wavelength), α is the phase shift, and C is the vertical offset. ... Template:Otherusescccc A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... In statistics, linear regression is a regression method that allows the relationship between y, the dependent, or response, variable, and the x, the independent, or explanatory, variable, in the case, where the model can be written as where is the matrix representing the independent variable and is a vector representing...

Probabilistic nature of fatigue

As coupons sampled from a homogeneous frame will manifest variation in their number of cycles to failure, the S-N curve should more properly be an S-N-P curve capturing the probability of failure after a given number of cycles of a certain stress. Probability distributions that are common in data analysis and in design against fatigue include the lognormal distribution, extreme value distribution and Weibull distribution. In probability and statistics, the log-normal distribution is the probability distribution of any random variable whose logarithm is normally distributed (the base of the logarithmic function is immaterial in that loga X is normally distributed if and only if logb X is normally distributed). ... Extreme value theory is a branch of statistics dealing with the extreme deviations from the median of probability distributions. ... In probability theory and statistics, the Weibull distribution (named after Waloddi Weibull) is a continuous probability distribution with the probability density function where and is the shape parameter and is the scale parameter of the distribution. ...

Complex loadings

Spectrum loading

In practice, a mechanical part is exposed to a complex, often random, sequence of loads, large and small. In order to assess the safe life of such a part: Spectrum (random) stress history. ... Spectrum (random) stress history. ... Random redirects here. ...

1. Reduce the complex loading to a series of simple cyclic loadings using a technique such as rainflow analysis;
2. Create an histogram of cyclic stress from the rainflow analysis;
3. For each stress level, calculate the degree of cumulative damage incurred from the S-N curve; and
4. Combine the individual contributions using an algorithm such as Miner's rule.

Figure 1: Uniform alternating loading The rainflow-counting algorithm (also known as the rain-flow counting method) is used in the analysis of fatigue data in order to reduce a spectrum of varying stress into a set of simple stress reversals. ... In statistics, a histogram is a graphical display of tabulated frequencies. ...

Miner's rule

In 1945, M. A. Miner popularised a rule that had first been proposed by A. Palmgren in 1924. The rule, variously called Miner's rule or the Palmgren-Miner linear damage hypothesis, states that where there are k different stress magnitudes in a spectrum, S_i (1 ≤ i ≤ k), each contributing n_i(S_i) cycles, then if N_i(S_i) is the number of cycles to failure of a constant stress reversal S_i, failure occurs when: Year 1945 (MCMXLV) was a common year starting on Monday (the link is to a full 1945 calendar). ... Year 1924 (MCMXXIV) was a leap year starting on Tuesday (link will display the full calendar). ...

C is experimentally found to be between 0.7 and 2.2. Usually for design purposes, C is assumed to be 1.

This can be thought of as assessing what proportion of life is consumed by stress reversal at each magnitude then forming a linear combination of their aggregate.

Though Miner's rule is a useful approximation in many circumstances, it has two major limitations:

1. It fails to recognise the probabilistic nature of fatigue and there is no simple way to relate life predicted by the rule with the characteristics of a probability distribution.
2. There is sometimes an effect in the order in which the reversals occur. In some circumstances, cycles of high stress followed by low stress cause more damage than would be predicted by the rule.

Paris' Relationship

Paris derived relationships for the stage II crack growth with cycles N, in terms of the cyclical component ΔK of the Stress Intensity Factor K Stress Intensity Factor, K, is used in fracture mechanics to more accurately predict the stress state (stress intensity) near the tip of a crack (crack tip) caused by a remote load or residual stresses. ...

where 2a is the crack length and m is typically in the range 3 to 5.

This relationship was later modified (by Forman, 1967[1]) to make better allowance for the mean stress, by introducing a factor depending on (1-R) where R = min. stress/max stress, in the denominator..

Low-cycle fatigue

Where the stress is high enough for plastic deformation to occur, the account in terms of stress is less useful and the strain in the material offers a simpler description. Low-cycle fatigue is usually characterised by the Coffin-Manson relation (popularised by L. F. Coffin in 1979 based on S. S. Manson's 1960 work): For other uses, see Plasticity. ... Look up strain in Wiktionary, the free dictionary. ... For the song by The Smashing Pumpkins, see 1979 (song). ... 1960 (MCMLX) was a leap year starting on Friday (the link is to a full 1960 calendar). ...

-where:

• Δε_p /2 is the plastic strain amplitude;
• ε_f' is an empirical constant known as the fatigue ductility coefficient, the failure strain for a single reversal;
• 2N is the number of reversals to failure (N cycles);
• c is an empirical constant known as the fatigue ductility exponent, commonly ranging from -0.5 to -0.7 for metals.

Fatigue and fracture mechanics

The account above is purely phenomenological and, though it allows life prediction and design assurance, it does not enable life improvement or design optimisation. For the latter purposes, an exposition of the causes and processes of fatigue is necessary. Such an explanation is given by fracture mechanics in four stages.

1. Crack nucleation;
2. Stage I crack-growth;
3. Stage II crack-growth; and
4. Ultimate ductile failure.

Factors that affect fatigue-life

Magnitude of stress including stress concentrations caused by part geometry.

Quality of the surface; surface roughness, scratches, etc. cause stress concentrations or provide crack nucleation sites which can lower fatigue life depending on how the stress is applied. For example, shot peening puts the surface in a state of compressive stress which inhibits surface crack formation thus improving fatigue life. Other surface treatments, such as laser peening, can also introduce surface compressive stress and could increase the fatigue life of the component. This improvement is normally observed only for high-cycle fatigue. Little improvement is obtained in the low-cycle fatigue régime. Shot peening is a process used to produce a decorative finish and to modify mechanical properties of metals. ...

The most recent development in the field of surface treatments utilizes ultrasonic energy to create residual compressive stresses that surpass those achieved by shot peening, laser peening, and other legacy methods. Ultrasonic Impact Technology operates within the harmonic frequency range of metals, allowing energy to be delivered deep into the material. Low amplitudes ensure that the metal is not overworked. ^{[citation needed]}

Material Type. Certain materials, such as steel, will never fail due to fatigue if the stresses remain below a certain level. Other materials, such as aluminum, will eventually fail due to fatigue regardless of the stresses the material sees.

Surface defect geometry and location. The size, shape, and location of surface defects such as scratches, gouges, and dents can have a significant impact on fatigue life.

Significantly uneven cooling, leading to a heterogeneous distribution of material properties such as hardness and ductility and, in the case of alloys, structural composition.

Size, frequency, and location of internal defects. Casting defects such as gas porosity and shrinkage voids, for example, can significantly impact fatigue life.

In metals where strain-rate sensitivity is observed (ferrous metals, copper, titanium, etc.) strain rate also affects fatigue life in low-cycle fatigue situations.

For non-isotropic materials, the direction of the applied stress can affect fatigue life.

Grain size; for most metals, fine-grained parts exhibit a longer fatigue life than coarse-grained parts.

Environmental conditions and exposure time can cause erosion, corrosion, or gas-phase embrittlement, which all affect fatigue life.

The operating temperature over which the part is exposed to affects fatigue life.

Design against fatigue

Dependable design against fatigue-failure requires thorough education and supervised experience in structural engineering, mechanical engineering, or materials science. There are three principal approaches to life assurance for mechanical parts that display increasing degrees of sophistication: Taipei 101, the worlds tallest building as of 2004. ... Mechanical engineers design and build engines and power plants. ... The Materials Science Tetrahedron, which often also includes Characterization at the center Materials science is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. ...

1. Design to keep stress below threshold of fatigue limit (infinite lifetime concept);
2. Design (conservatively) for a fixed life after which the user is instructed to replace the part with a new one (a so-called lifed part, finite lifetime concept, or "safe-life" design practice);
3. Instruct the user to inspect the part periodically for cracks and to replace the part once a crack exceeds a critical length. This approach usually uses the technologies of nondestructive testing and requires an accurate prediction of the rate of crack-growth between inspections. This is often referred to as damage tolerant design or "retirement-for-cause".

// Nondestructive testing (also called NDT, nondestructive evaluation, NDE, and nondestructive inspection, NDI) is testing that does not destroy the test object. ... In science, engineering, industry and statistics, accuracy is the degree of conformity of a measured or calculated quantity to its actual, nominal, or some other reference, value. ...

Famous fatigue failures

Versailles accident

On May 8, 1842 one of the trains carrying revellers on their return from Versailles to Paris, having witnessed the celebrations of the birthday of Louis Philippe, derailed and caught fire. Though the resulting conflagration mutilated the dead beyond recognition or enumeration, it is estimated that 53 perished and around 40 were seriously injured. May 8 is the 128th day of the year in the Gregorian Calendar (129th in leap years). ... 1842 was a common year starting on Saturday (see link for calendar). ... Versailles (pronounced , in French), formerly the de facto capital of the kingdom of France, is now a wealthy suburb of Paris and is still an important administrative and judicial center. ... City flag City coat of arms Motto: Fluctuat nec mergitur (Latin: Tossed by the waves, she does not sink) Paris Eiffel tower as seen from the esplanade du Trocadéro. ... Louis-Philippe of France (October 6, 1773–August 26, 1850), served as the Orleanist king of the French from 1830 to 1848. ... It has been suggested that this article or section be merged with Flame. ...

The derailment had been the result of a broken locomotive axle and Rankine's investigation highlighted the importance of stress concentration for the first time. Great Western Railway No. ... William John Macquorn Rankine (July 2, 1820 - December 24, 1872) was a Scottish engineer and physicist. ...

De Havilland Comet

Metal fatigue came strongly to the notice of aircraft engineers in 1954 after three de Havilland Comet passenger jets had broken up in mid-air and crashed within a single year. Investigators from the Royal Aircraft Establishment at Farnborough in England told a public enquiry that the sharp corners around the plane's window openings (actually the forward ADF antenna window in the roof) acted as initiation sites for cracks. All aircraft windows were immediately redesigned with rounded corners. Year 1954 (MCMLIV) was a common year starting on Friday of the Gregorian calendar. ... The de Havilland Comet of Britain was the worlds first commercial jet airliner. ... This article needs cleanup. ... Farnborough is a town in the Hampshire borough of Rushmoor in South East England. ... Motto: (French for God and my right) Anthem: God Save the King/Queen Capital London (de facto) Largest city London Official language(s) English (de facto) Unification    - by Athelstan AD 927  Area    - Total 130,395 km² (1st in UK)   50,346 sq mi  Population    - 2006 est. ... A stress concentration is a phenomenon encounterered in mechanical engineering where an object under load has higher than average local stresses due to its shape. ...

Others

• The Liberty Ships during World War II
• Capsize of the oil platform Alexander Kielland
• United Airlines Flight 232, Japan Airlines Flight 123, China Airlines Flight 611, and Aloha Airlines Flight 243
• The Boston Molasses Disaster has been attributed to a fatigue failure
• The 1998 Eschede train disaster (crash of an InterCityExpress train).

The Liberty ships were cargo ships built in the United States during World War II. They were cheap and quick to build, and came to symbolize U.S. wartime industrial output. ... Combatants Allied powers: United Kingdom Soviet Union United States Republic of China and others Axis powers: Germany Italy Japan and others Commanders Winston Churchill Joseph Stalin Franklin Roosevelt Chiang Kai-shek Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000,000 Total... Alexander Kielland was a Norwegian oil platform in the Ekofisk field. ... United Airlines Flight 232 was a scheduled flight operated by United Airlines between Denver and Philadelphia via Chicago. ... Japan Airlines Flight 123 was a JAL domestic flight from Tokyo International Airport in Haneda to Osaka International Airport in Itami, Hyogo. ... China Airlines Flight 611 (CAL611, CI611) flew from Chiang Kai Shek International Airport in Taipei, Taiwan to Hong Kong International Airport in Hong Kong, China. ... Aloha Airlines Flight 243 was a scheduled Aloha Airlines Boeing 737-200 flight between Hilo and Honolulu in Hawaii. ... Aftermath of the disaster The Boston Molasses Disaster which is also known as the Great Molasses Flood or The Great Boston Molasses Tragedy occurred on January 15, 1919, in the North End neighborhood of Boston, Massachusetts in the United States. ... 1998 (MCMXCVIII) was a common year starting on Thursday of the Gregorian calendar, and was designated the International Year of the Ocean. ... This picture illustrates the destruction of the rear passenger cars. ... 3rd Generation ICE train The InterCityExpress or ICE is a high-speed train, built by Siemens AG and others, operated mainly in Germany and neighboring countries, for example to Zürich, Switzerland or Vienna, Austria. ...

See also

• Fracture mechanics
• Air safety
• Structural failure
• Materials science
• Peening
• Shock (mechanics)
• Corrosion fatigue
• Vibration

This does not cite its references or sources. ... Air safety is a broad term encompassing the theory, investigation and categorization of flight failures, and the prevention of such failures through appropriate regulation, as well as through education and training. ... Structural failure refers to loss of the load-carying capacity of a component or member within the structure or of the structure itself. ... The Materials Science Tetrahedron, which often also includes Characterization at the center Materials science is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. ... A 380 mm (15 in) ball-peen hammer. ... In mechanics, a shock is a sudden acceleration or deceleration caused, for example, by impact or explosion. ... Wikipedia does not have an article with this exact name. ... Look up vibration in Wiktionary, the free dictionary. ...

References

1. ^ ^{a b} W. Schutz (1996). A history of fatigue. Engineering Fracture Mechanics 54: 263-300. DOI
2. ^ W.J.M. Rankine. (1842). "On the causes of the unexpected breakage of the journals of railway axles, and on the means of preventing such accidents by observing the law of continuity in their construction". Institution of Civil Engineers, Minutes of Proceedings, 105-108.
3. ^ F. Braithwaite. (1854). "On the fatigue and consequent fracture of metals". Institution of Civil Engineers, Minutes of Proceedings, 463–474.

• Andrew, W. (1995) Fatigue and Tribological Properties of Plastics and Elastomers, ISBN 1-884207-15-4
• Dieter, G. E. (1988) Mechanical Metallurgy, ISBN 0-07-100406-8
• Little, R. E. & Jebe, E. H. (1975) Statistical design of fatigue experiments ISBN 0-470-54115-6

External links

• Fatigue by Shawn M. Kelly
• SAE Fatigue, Design, and Evaluation Committee website
• A collection of fatigue knowledge and calculators